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Main Group 43: (G)Buzz
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Sub Id  Contents

01      Basic Instrument
    1   LINEN envelope, automatic inh
    1B  LINEN envelope, constant inh
    2   EXPON envelope
    3   EXPSEG envelope
    
21      Kratio envelope
    1   LINEN envelope

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Overview

BUZZ and GBUZZ are pulse generators and provide yet another means
of effectively generating a complex audio signal. Using the
closed form of a sum of sinusoids, only two oscillators are able
to produce a complex wave of N partials. In the case of BUZZ, it
is a set of harmonically related cosine partials of the
fundamental frequency ifqc. For their spectral richness, pulse
generators are particularly useful as sources in subtractive
synthesis designs.

BUZZ is a special case of the more general GBUZZ in which all
harmonics are equally strong, and the series starts with the
fundamental. 

In GBUZZ one can chose an exponential coefficient multiplier
'kratio' to envelope the harmonic spectrum (One cannot use the
variable 'kr' for this ratio, as suggested in the Csound manual;
'kr' is a reserved symbol) of the output. Also GBUZZ allows to
specify a lowest harmonic 'klh' different from the fundamental
frequency. 

A pulse train is obtained by extending the number of harmonics up
to the Nyquist frequency. This is done by making the number of
harmonics frequency dependent: 

                  knh = int (sr/2/ifqc).

In general pulse waveforms have a significant amplitude only
during a short interval of time (pulse width).
Repeated periodically, the pulse waveform yields rich spectra,
depending on period and shape of the pulse. The pulse width gets
narrower with increasing number of harmonics in the spectrum.

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Suggested Reading

Dodge, C, and T.A. Jerse 1985.
"Introduction to Discrete Summation Formulae."
Computer Music: Synthesis, Composition and Performance. 
Schirmer Books. pp. 149-153, 156-157.

Moorer, J.A. 1976.
"The Synthesis of Complex Audio Spectra by Means of Discrete
Summation Formulae."
Journal of the Audio Engineering Society 24:717-727.

Moorer, J.A. 1985.
"Signal Processing Aspects of Computer Music: A Survey."
chapter: "Discrete Summation Formulae."
in J. Strawn, ed. 1985.
Digital Audio Signal Processing: An Anthology. 
A-R Editions, pp. 180-193.

Winham, Godfrey, and Kenneth Steiglitz 1970.
"Input Generators for Digital Sound Synthesis."
Journal of the Acoustical Society of America 47(2):665-666.     

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43_01_1
additional parameters: none


This instrument simply shows the effect of varying fundamental
frequency on the tone quality, when the number of harmonics is
automatically calculated by
             
            inh = int (sr/2/ifqc)

The tone is played in six consecutive octaves. It turns out to be
rather buzzy for low frequencies, which explains the name of this
unit generator. The timbre becomes brighter in the high frequency
area.

(flowchart)
(.orc and .sco files)

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43_01_1B
additional parameters: none


This time the number of harmonics is constant at 10 per note. The
timbre of the tones is more steady, compared to 43_01_1. As the
number of harmonics is not put in relation to the sampling rate,
the last note contains objectionable, ugly foldover components.


(flowchart)
(.orc and .sco files)

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43_01_2
additional parameters:


Same as 43_01_1, this time with an EXPON envelope. 


(flowchart)
(.orc and .sco files)

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43_01_3
additional parameters:


One hears the BUZZ with an EXPSEG envelope. The instrument plays
the same sequence as the two instruments before.

(flowchart)
(.orc and .sco files)

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43_21_1
additional parameters: none

The run gives the effect on GBUZZ of varying kratio during
performance (values around unity). For this, LINSEG creates a
kratio envelope varying with the duration of the note.

A long note of 10 seconds is followed by three shorter notes.
This is a very interesting way to control changes in tone colour. 

(flowchart)
(.orc and .sco files)
